Topic
Toric variety
About: Toric variety is a research topic. Over the lifetime, 2630 publications have been published within this topic receiving 65604 citations. The topic is also known as: torus embedding.
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TL;DR: In this paper, a simple class of Calabi-Yau 3-folds with smooth ambient spaces is studied and all positive monad bundles with SU(N), N = 3,4,5 structure groups, subject to the heterotic anomaly cancellation constraint.
Abstract: We systematically approach the construction of heterotic E_8 X E_8 Calabi-Yau models, based on compact Calabi-Yau three-folds arising from toric geometry and vector bundles on these manifolds. We focus on a simple class of 101 such three-folds with smooth ambient spaces, on which we perform an exhaustive scan and find all positive monad bundles with SU(N), N=3,4,5 structure groups, subject to the heterotic anomaly cancellation constraint. We find that anomaly-free positive monads exist on only 11 of these toric three-folds with a total number of bundles of about 2000. Only 21 of these models, all of them on three-folds realizable as hypersurfaces in products of projective spaces, allow for three families of quarks and leptons. We also perform a preliminary scan over the much larger class of semi-positive monads which leads to about 44000 bundles with 280 of them satisfying the three-family constraint. These 280 models provide a starting point for heterotic model building based on toric three-folds.
20 citations
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20 citations
18 Mar 2006
TL;DR: A survey of the recent results about quasi-maps as well as their applications in different branches of representation theory and algebraic geometry can be found in this paper, where the authors consider the case when X is a (partial)flag variety of a semi-simple algebraic group G (or, more generally, of any symmetrizable Kac).
Abstract: Given a projective variety X and a smooth projective curve C one may consider the
moduli space of maps C �¨ X. This space admits certain compactification whose points are
called quasi-maps. In the last decade it has been discovered that in the case when X is a (partial)
flag variety of a semi-simple algebraic group G (or, more generally, of any symmetrizable Kac.
Moody Lie algebra) these compactifications play an important role in such fields as geometric
representation theory, geometric Langlands correspondence, geometry and topology of moduli
spaces of G-bundles on algebraic surfaces, 4-dimensional super-symmetric gauge theory (and
probably many others). This paper is a survey of the recent results about quasi-maps as well as
their applications in different branches of representation theory and algebraic geometry.
20 citations
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TL;DR: In this paper, the authors give an elementary approach to proving the birationality of multiple Berglund-H\"ubsch-Krawitz (BHK) mirrors by using Shioda maps.
Abstract: We give an elementary approach to proving the birationality of multiple Berglund-H\"ubsch-Krawitz (BHK) mirrors by using Shioda maps. We do this by creating a birational picture of the BHK correspondence in general. Although a similar result has been obtained in recent months by Shoemaker, our proof is new in that it sidesteps using toric geometry and drops an unnecessary hypothesis. We give an explicit quotient of a Fermat variety to which the mirrors are birational.
20 citations
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TL;DR: In this paper, an equivariant generalization of Ehrhart theory is proposed for lattice points in dilations of lattice polytopes, and the character formula of Procesi, Dolgachev, Lunts and Stembridge for the action of Weyl group on the cohomology of a toric variety associated to a root system.
20 citations